How to place the right seams for the UV mapping of a curvy object like this?
I'm not at all an expert in unwrapping, but I'd say the trick is not so much in the seam placement, but more in the top geometry of the mesh where all the loops meet.

Make sure you have an all quads mesh that doesn't end in a triangle fan.

If you are not sure what I mean, try this:

1) Select the top vertex and delete it.

2) Select the first open edge loop, extrude it and right click to cancel (leave it in place).

3) Scale it to zero to make it meet at the center. 
You may move it slightly up in Z to compensate so it's not perfectly flat.
Make sure you don't remove doubles so you have a quad's only mesh.

4) Lastly you can use the Unwrap > Follow Active Quads > Lenght Average to have an even rectangular unwrap.